Altered chords are a special category of chords that - as the name implies - alter other chords. There are, for example, altered dominant seventh chords with a flattened or a sharp fifth: 7-5 and 7+5.
See diagrams of altered chords:
C7-5 D7-5 E7-5 F7-5 G7-5 A7-5 B7-5
C7+5 D7+5 E7+5 F7+5 G7+5 A7+5 B7+5
C7-9 D7-9 E7-9 F7-9 G7-9 A7-9 B7-9
C7+9 D7+9 E7+9 F7+9 G7+9 A7+9 B7+9
Theory of this chord category are presented here.
We can compare a normal dominant seventh chord with altered dominant chords in the note of C:
C7: C – E – G – Bb
C7-5 (C7b5): C – E – Gb – Bb
C7+5 (C7#5): C – E – G# – Bb
Concerning chord names, instead of minus (-), flat (b) are sometimes used and instead of plus (+), sharp (#) are sometime used. Therefore, C7-5 and C7b5 is the same chord and C7+5 and C7#5 is the same chord. Note also that C7+5 contains the same notes as Caug7.
Comparing a normal dominant seventh chord with another pair of altered chords.
C7: C – E – G – Bb
C7-9 (C7b9): C – E – G – Bb – Db
C7+9 (C7#9): C – E – G – Bb – D#
The names of these chords are C dominant seventh, sharp ninth and C dominant seventh, flat ninth. C7-9 and C7+9 could also be written C7b9 and C7#9 respectively.
Comparing with a third group of altered seventh chords.
C7: C – E – G – Bb
C7+11 (C7#11): C – E – G – Bb – F#
The name of this chord is C dominant seventh, sharp eleventh (a correspondent C dominant seventh, eleventh flat ninth does not exist). C7+11 could also be written C7#11.
Finally, lets look at some less common categories.
Altered ninth and thirteenth chords.
C9#11: C – E – G – Bb – D – F#
C13b9: C – E – G – Bb – Db – F – A
C13#11: C – E – G – Bb – D – F# – A
Continued reading: altered chords as substitutions and Altered chord on Wikipedia
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