Probiotics are basically 'friendly bacterias'. They exist in us naturally to aid digestion and strengthen immunity. Taking antibiotics will kill them and certain diets will be less friendly to them (e.g. a diet very high in sugars that may cause candida/thrush to flourish).
You find them in live yoghurts - like activa, Rachel's yoghurts. Anything that says 'bio' 'live'. The bacterias have various names like Lacto acidophilus, Lactobacillus casei and Bifidobacterium species.
There are also in yoghurt drinks like yakult, proactiva.
Health food shops like Holland and Barrett will also sell capsules containing probiotics like lacto acidophilus.
However - not all these things may be suitable for your LO e.g dairy based stuff. You could start by visiting a health food shop and asking for advice.