The C7(#11) is a dominant 7th chord, extended by an augmented 4th. Because the augmented 4th is a chord extension (it doesn’t belong to the basic chord consisting of root – 3rd or sus2 or sus4 – 5th – 7th or 6th), it is written as #11 in the chord symbol.
The C7(#11) consists of the tones C (1), E (3), G (5), Bb (7) and F# (#11). The 5th G will normally be dropped for the #11 that is located 1 half-step (1 fret) below and also doesn't sounds desirable here.
The #11 actually belongs to the group of altered tensions (like b9, #9 and b13), but it is interestingly most used where the other tensions should be played in there natural form (9, 13). This is the case when the dominant 7th chord doesn‘t resolve from V to I, like in the progression Fmaj7 Bb7(#11) Cmaj7 Am7 or the progression Fmaj7 G7(#11) Gm7 C7(9) Fmaj7.
The most common application is the so called tritone substitution („sub five“): in a II-V-I progression the V7 chord is replaced ba a bII7(#11) chord, for example Dm7 Db7(#11) Cmaj7 is played instead of Dm7 G7(alt) Cmaj7. By the way, a Db7(#11) has the same tones as a G7(#11)!