Tingly feelings are similar to (and my overlap) warm fuzzy feelings. They are physical sensations produced by an emotional or spiritual experience. It feels like all your cells are alive and happy.
In certain types of yoga (and other related spiritual disciplines), tingly feelings are associated with certain chakras and have a deeper significance. For most people though, tingly feelings just feel really nice. :-)
As examples, tingly feelings may be produced by having a loved one gently stroking their finger along your back, by experiencing something serene and beautiful, or through meditation. Every person is slightly different, and may experience tingly feelings in response to different stimuli, or even not at all.