I think this is often counted as an advanced topic but it is really useful so I shall go through it here.
All physical formulas have to be consistent in units. For example if we have Force = Mass times Acceleration (F = ma) then the units of force must be Kg m sec^-2 which it is (by definition in this case). If the units did not match then we would know that the formula was wrong. Therefore we know that the formula is not definitely wrong but not necessarily correct.
I often use this if I am in a hurry and need to do something like convert KWhours (Kilowatt Hours) for a given length of time into average power output (in Kilowatts). Do I multiply or divide? A quick look at the units (power x time) tells me to divide by the time to leave the units for power (in Kilowatts).

For another more complicated example if we have some equation for energy it must have the units of energy – even if it is not immediately obvious.
Let us take E = mc² – energy equals mass times the speed of light squared. Energy is units of joules which is a derived unit and is really Kg m² / sec²
On the right hand side of the equation we have mass (measured in Kg) times the speed of light (measured in m/s) squared – i.e. Kg m² / sec². The units on both sides match up so we know the formula is not definitely wrong.

However, the formula is wrong in certain cases. This famous formula only applies when the object and observer and not moving relative to each other. If they are moving relative to each other, then the formula is

where c is the speed of light and v is the velocity of the object relative to the observer. If there is no relative movement then v is zero and the formula becomes E = mc²
Since cn and v have the same units then the denominator is dimensionless and the dimensional analysis fails.