For chickens it's ones that are classed as 'barn' rather than free range. There isn't actually much of a difference between the two but free range chickens tend to have access to outside (they generally choose to stay inside though for some reason 
) and a bit more space. I think it's the sheer volume that they can be produced in that gives them the 'factory' label.
For pigs I imagine that again it's that they are housed in large volumes inside on 'slats' (basically concrete with holes in it to let the waste drain away) and reared intensively with little access to outside space.
There's been a slight trend in dairy farming to go down what is called a 'zero grazing' route. Basically the dairy cows are housed all year round (most cattle are housed inside over winter anyway for welfare reasons) but for dairy cows this is extended through summer as well so that diet etc can be carefully controlled to maximise milk yields. Most people, who have gone down this route have also invested in robotic milking where basically the cows walk themselves in to a rotating milking parlour and they are then milked by very clever robotic arms. Again, it's usually the sheer volume of some of these 'units' that gives it the name 'factory farming' rather than the actual methods used.
I believed there is some controversy around certain methods in dairy industry around artificial insemination and the use of 'rape racks'. AI is no more stressful for a cow than being inseminated the natural way by a bull (and actually is far less risky for both the cow and the bull, it's not unheard of for either bulls or cows to break legs during bulling!) Dairy cows have also been bred to not be particularly maternal and generally have calves taken away from them very early on to prevent bonding. The calves are then reared by humans, some male dairy calves are shot at birth as there is no market for them unless people start eating high welfare veal, most male calves do go for beef production. Artificially inseminating dairy cows with 'sexed semen' to increase the likelihood of getting a female calf is also increasingly common.
To be honest I don't know whether the people who own the mega chicken/dairy/pig units would consider themselves farmers these days or if they are just business people. Certainly they operate on such a scale that it's not what most family farmers (the vast majority of meat producers still in the UK) would recognise as farming.
Either way though if people want to continue to consume meat and don't want 'factory farming' to become the norm then they need to put their money where their mouth is and demand high welfare meat and be prepared to pay a fair price for it in the shops.
If everyone went vegetarian it genuinely wouldn't bother me, I would find that far preferable to the current situation where people want high welfare meat but aren't prepared to pay for it and which allows factory farming to become the only way the demand for cheap meat can be met.
European Farming subsidies that basically top up the incomes of current family farms and allow them to produce high welfare meat at prices the public are prepared to pay are set to end in 2021/22 with Brexit so it will be interesting to see what happens to UK meat production then.