The majority include one that is damp (5)
I believe the answer is:
moist
'is damp' is the definition.
(synonyms)
'the majority include one' is the wordplay.
'the majority' becomes 'most' (most of a group).
'include' means one lot of letters goes inside another.
'one' becomes 'i' (Roman numeral).
'most' going around 'i' is 'MOIST'.
'that' is the link.
(Other definitions for moist that I've seen before include "Damp, humid" , "Slightly wet, damp" , "Affected by tears, perhaps" , "sloppy" , "lubricated" .)