You get a gift membership, free t-shirt, and I some extra privileges related to creating tournaments, vacation time, and seeing other players' stats. Mostly I just wanted to support the excellent work the chess.com team's doing.
Gold vs. Platinum membership

Silver is the one that pays monthly, $5 per. It has the same benefits as Gold, so Gold is a good deal over that if you anticipate using the site for any length of time.
Platinum, however, is $50 MORE than gold -- i.e., $80. Quite a jump.

Platinum is $6.66 per month, not that high above silver at about $5 per month.
Personally, I'm not really in need of a chess.com T-shirt ($20 value) or a gift membership ($30 yearly). If those were deducted from a platinum membership, I'd immediately switch to platinum.
I really enjoy the site, so I feel I should support it, but functionally, I'd want the extra tournament features - the inability to make multiple-round tournaments is really a limit on tournament creation, if you don't want to play every registered opponent at once.
I think gold membership is really cool, and I plan to get it soon. You get a lot of features. However, platinum membership costs a lot more than gold membership!
Do platinum members get that many features over gold members?
Maybe you can take out the 'gift membership feature' and make platinum cost less? Platinum-gold= $50. If it was like that I would buy platinum, but for now, I'm just getting a gold membership.
Chess.com is great! Keep up the good work!