If you have a connecting flight then you need to re-check your baggage at each airport.
Even if your connecting flight is with the same budget airline, you still need to re-check your baggage during the layover. Some legacy carriers will be able to book your checked baggage all the way through to your final destination and they will inform you if this is possible when they take the baggage.
The rechecking process means leaving the transit zone to pick up your baggage, delivering it to the next airline counter and then passing through security and immigration. This means there are visa implications for some passengers so please book your flights with care.
We always try to allow our passengers at least a two hour layover between flights. If you only have cabin baggage you do not need to worry about re-checking it.