On a precision approach (ILS) you have a Decision Altitude (DA). On a non-precision approach (Localiser, VOR, NDB, SRA) you have a Minimum Descent Altitude (MDA). Basically the difference is as follows:
DA: You make a decision NO LATER THAN the DA and if that decision is "go-around" you commence an immediate go-around and Missed Approach Procedure (MAP). It is accepted that you will descend slightly below the DA even if you start the go-around perfectly on time, but that this dip is typically going to be less than 50'and will not adversely affect obstacle clearance. The dip below DA is factored into the performance planning calculations used during the creation of the approach.
MDA: You must NOT descend below this altitude at any time unless you have the appropriate minimum visual references required to continue visually. In order to avoid going below MDA you must effectively make the decision to discontinue the approach a little way above MDA in order to give yourself time to level off at or just above MDA (up to 100' above on your IRT!). You normally need to allow 50-100' above MDA to give yourself time to level off without breaking the MDA. If you decide to discontinue the approach on a non-precision approach, you can level at (or just above) the MDA and continue to track inbound in the hope that you will acquire the runway visually and therefore make a visual approach and landing. However, you may not continue inbound any further than the Missed Approach Point (MAPt) which will be specified on the approach plate (typically the threshold/0 DME) at which point you must commence a go-around.
In practice, many airlines (especially jet operators) do not level off and track to the MAPt - if they are not visual by the time they get to the MDA they commence an immediate go-around. This is because once you level a 737-type aeroplane (or larger!) at MDA the inertia or the aeroplane makes it highly unlikely that you will be able to effect a safe landing.
Hope that answers your question!