WikipediaWikipedia explains this rather well WIKI but I'll pick out the relevant stuff for you.
Before the Geiger–Marsden experiment, the general idea was that atoms were buildbuilt of some permeable positive substrate in which some negative particles were floating around,around; the so called plum puddingplum-pudding model.
If we shoot $\alpha$ particles on this setup they should all pass troughthrough the atoms since the positive substrate is thought to be permeable ! (left side of the figure)
But when people did the experiment they saw that most particles went troughthrough while some scattered $180^\circ$ backwards, some even bent a small angle ! (right side of the figure)
The plum pudding-pudding model had no problem with the particles that went troughthrough undisturbed but what about the ones that were backscattered ? peoplePeople theorized that there must be some solid core in the atom against which the $\alpha$ particles could scatter. The core couldn't be too big since only a small fraction of the $\alpha$ particles backscattered.
This leads to a model in which most of the mass (to which $\alpha$ particles can scatter) are in the center of the atom with the negative charges around it!