Apple seed and apple core at home (6)
I believe the answer is:
pippin
'apple' is the definition.
(pippin is a kind of apple)
'seed and apple core at home' is the wordplay.
'seed' becomes 'pip' (as in a fruit pip).
'and' means one lot of letters go next to another.
'core' means to look at the middle letters.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
The central letter of 'apple' is 'p'.
'pip'+'p'+'in'='PIPPIN'
(Other definitions for pippin that I've seen before include "excellent example" , "fruit" , "Hobbit, friend of 1 across" , "beauty" , "Kind of eating apple" .)