Start with the basics, adding ammonia to bromoethane...
The lone pair on the N attacks the delta positive C next to the Br and ethylamine forms: NH2CH2CH3; that should look a bit funny, but bare with me. Simple SN2, so far.
Start again with methylamine instead of ammonia and there is still a lone pair on the N, so SN2 once again andCH3NHCH2CH3.
But, there is still a lone pair on the N, so we can go again: CH3N(CH2CH3)2 forms.
BUT, there is still a lone pair, so off we go again: CH3N+(CH2CH3)3