I very much enjoy reading the "What Is...?" column in the Notices of the AMS. While looking for an index to this column I stumbled across somebody who actually created one (Thumbs up to Armin Straub who put it together):

1. What is...an amoeba? — Oleg Viro, September 2002
2. What is...the monster? — Richard Borcherds, October 2002
3. What is...a building? — Kenneth S. Brown, November 2002
4. What is...an alteration? — Frans Oort, December 2002
5. What is...a shtuka? — David Goss, January 2003
6. What is...a gerbe? — Nigel Hitchin, February 2003
7. What is...a train track? — Lee Mosher, March 2003
8. What is...a stack? — Dan Edidin, April 2003
9. What is...a worm? — Harold Boas, May 2003
10. What is...a bubble tree? — Thomas Parker, June/July 2003
11. What is...a dessin d'enfant? — Leonardo Zapponi, August 2003
12. What is...a curvelet? — Emmanuel Candès, December 2003
13. What is...a quasi-morphism? — D. Kotschick, February 2004
14. What is...a billiard? — Yakov Sinai, April 2004
15. What is...a free lunch? — Fredy Delbaen and Walter Schachermayer, May 2004
16. What is...an operad? — James Stasheff, June/July 2004
17. What is...an expander? — Peter Sarnak, August 2004
18. What is...a grope? — Peter Teichner, September 2004
19. What is...a topos? — Luc Illusie, October 2004
20. What is...a motive? — Barry Mazur, November 2004
21. What is...a flip? — Alessio Corti, December 2004
22. What is...an open book? — Emmanuel Giroux, January 2005
23. What is...a brane? — Gregory Moore, February 2005
24. What is...a dimer? — Richard Kenyon and Andrei Okounkov, March 2005
25. What is...a horseshoe? — Mike Shub, May 2005
26. What is...property tau? — Alex Lubotzky, June/July 2005
27. What is...a compacton? — Philip Rosenau, August 2005
28. What is...a Lefschetz pencil? — Robert Gompf, September 2005
29. What is...a pseudoholomorphic curve? — Simon Donaldson, October 2005
30. What is...a Gröbner basis? — Bernd Sturmfels, November 2005
31. What is...a random matrix? — Persi Diaconis, December 2005
32. What is...a quantum group? — Shahn Majid, January 2006
33. What is...a graph minor? — Bojan Mohar, March 2006
34. What is...a syzygy? — Roger Wiegand, April 2006
35. What is...percolation? — Harry Kesten, May 2006
36. What is...a coarse space? — John Roe, June/July 2006
37. What is...a strange attractor? — David Ruelle, August 2006
38. What is...a quasicrystal? — Marjorie Senechal, September 2006
39. What is...a bad end? — Charles Epstein, October 2006
40. What is...Turing reducibility? — Martin Davis, November 2006
41. What is...a quasiconformal mapping? — Juha Heinonen, December 2006
42. What is...a projective structure? — William Goldman, January 2007
43. What is...a Young tableau? — Alexander Yong, February 2007
44. What is...a minimal model? — János Kollár, March 2007
45. What is...a tropical curve? — Grigory Mikhalkin, April 2007
46. What is...an infinite swindle? — Valentin Poénaru, May 2007
47. What is...a Galois representation? — Mark Kisin, June/July 2007
48. What is...a Higgs bundle? — Steve Bradlow, Oscar García-Prada, and Peter Gothen, September 2007
49. What is...a Woodin cardinal? — John Steel, October 2007
50. What is...Boy's surface? — Robion Kirby, November 2007
51. What is...a cluster algebra? — Andrei Zelevinsky, December 2007
52. What is...quantum chaos? — Ze?ev Rudnick, January 2008
53. What is...JPEG? — David Austin, February 2008
54. What is...a systole? — Marcel Berger, March 2008
55. What is...property A? — Piotr Nowak and Guoliang Yu, April 2008
56. What is...a toric variety? — Ezra Miller, May 2008
57. What is...forcing? — Thomas Jech, June/July 2008
58. What is...outer space? — Karen Vogtmann, August 2008
59. What is...an ∞-category? — Jacob Lurie, September 2008
60. What is...stable commutator length? — Danny Calegari, October 2008
61. What is...a cross ratio? — François Labourie, November 2008
62. What is...a period domain? — James Carlson and Phillip Griffiths, December 2008
63. What is...the Schwarzian derivative? — Valentin Ovsienko and Sergei Tabachnikov, January 2009
64. What is...a skein module? — W. B. Raymond Lickorish, February 2009
65. What is...Lehmer's number? — Eriko Hironaka, March 2009
66. What is...measure rigidity? — Manfred Einsiedler, May 2009
67. What is...an elliptic genus? — Serge Ochanine, June/July 2009
68. What is...the parity phenomenon? — John Friedlander and Henryk Iwaniec, August 2009
69. What is...the complex dual to the real sphere? — Simon Gindikin, September 2009
70. What is...Stanley depth? — M. R. Pournaki, S. A. Seyed Fakhari, M. Tousi, and S. Yassemi, October 2009
71. What is...a Legendrian knot? — Joshua M. Sabloff, November 2009
72. What is...a Rota-Baxter algebra? — Li Guo, December 2009
73. What is...an Oka manifold? — Finnur Larusson, January 2010
74. What is...a halting probability? — Cristian S. Calude and G. J. Chaitin, February 2010
75. What is...a Gaussian entire function? — Fedor Nazarov and Mikhail Sodin, March 2010
76. What is...a Wilf-Zeilberger pair? — Akalu Tefera, April 2010
77. What is...a perverse sheaf? — Mark Andrea de Cataldo and Luca Migliorini, May 2010
78. What is...a kinetic solution for degenerate parabolic-hyperbolic equations? — Gui-Qiang G. Chen and Benoît Perthame, June/July 2010
79. What is...a paraproduct? — Árpád Bényi, Diego Maldonado, and Virginia Naibo, August 2010
80. What is...a sandpile? — Lionel Levine, James Propp, September 2010
81. What is...a linear algebraic group? — Skip Garibaldi, October 2010
82. What is... cost? — Damien Gaboriau, November 2010
83. What is...a mock modular form? — Amanda Folsom, December 2010
84. What is... persistent homology? — Shmuel Weinberger, January 2011
85. What is...a free cumulant? — Jonathan Novak, Piotr Sniady, February 2011
86. What is... equivariant cohomology? — Loring W. Tu, March 2011
87. What is...a G2-manifold? — Spiro Karigiannis, April 2011
88. What is...a infra-nilmanifold endomorphism?? — Karel Dekimpe, May 2011
89. What is...a resplendent structure? — Roman Kossak, June/July 2011
90. What is...a derived stack? — Gabriele Vezzosi, August 2011
91. What is... Thompson's group? — J. W. Cannon, W. J. Floyd, September 2011
92. What is...a stationary measure? — Alex Furman, October 2011
93. What is...a natural proof? — Timothy Y. Chow, December 2011
94. What is...a Fenchel conjugate? — Heinz H. Bauschke, Yves Lucet, January 2012
95. What is...a pseudoconvex domain? — R. Michael Range, February 2012
96. What is...an affine sphere? — Daniel J. F. Fox, March 2012
97. What is... data mining? — Mauro Maggioni, April 2012
98. What is...an approximate group? — Ben Green, May 2012
99. What is...a biholomorphic mapping? — Eric Bedford, June/July 2012
100. What is...an octopus decomposition? — Larry Conlon, August 2012
101. What is... cop number? — Anthony Bonato, September 2012
102. What is...a scissors congruence? — Johan L. Dupont, October 2012
103. What is... essential dimension? — Zinovy Reichstein, November 2012
104. What is...a Shimura variety? — James S. Milne, December 2012
105. What is...a tensegrity? — Robert Connelly, January 2013
106. What is...a frame? — Christopher Heil, June/July 2013
107. What is...the p-adic Mandelbrot set? — Joseph H. Silverman, September 2013
108. What is...the Leech lattice? — Chuanming Zong, October 2013
109. What is...a flag algebra? — Alexander A. Razborov, November 2013
110. What is... cyclic sieving? — Victor Reiner, Dennis Stanton, and Dennis White, February 2014
111. What is...a spectrahedron? — Cynthia Vinzant, May 2014