'on the spot' means here and now, 'at this time and place'
The expression is often used with the verb 'put' : 'to put someone on the spot'.
For example 'I'm going to put you on the spot' means that you are about to ask someone a question that you want them to answer right away.
'He put me on the spot' : he asked me something, or asked me to do something, that I had not prepared for.
'I did it on the spot' : I did it there and then [at that time and place]