A diagonal spread is a spread which is a combination of a vertical spread, where the options are of the same expiry, but different strikes, and a horizontal spread, where the options are of the same strike, but different expiries. That is, a diagonal spread has two options of different expiries and strikes at the same time.
A tipical diagonal call spread would consist of a short position in an out-of-the-money call of a near expiry and a long position in a deeper out-of-the-money (that is, one that has a higher strike) call of a far expiry.
Tipically, for this diagonal spread at the expiry of the first call, another call of the same strike, but with the expiry of the second call is sold, thus converting the diagonal spread into a bear call spread.
The diagonal call spread can be used when you expect little volatility during the lifetime of the first call and somewhat bearish after that.
See also diagonal put spread, double diagonal, bear calendar spread.
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European call struck at 10.000 with expiry in 30 days
European call struck at 11.000 with expiry in 90 days
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