It's [significant, but not the main source of global warming](https://www.skepticalscience.com/how-much-meat-contribute-to-gw.html
). CO2 is now at about 405ppm, while methane is at 1.8 ppm. Even taking the highest multiplier for methane only gets you to 144 equivalent ppm. And there are many other sources for methane besides animal agriculture, including leakage from oil and natural gas wells.
It isn't so much what the cows produce but the volume of fossil fuels used to produce that pound of ground beef in your supermarket. You have to think of the entire supply chain from fertilizer to grow grass and corn, to pesticides for spraying weeds in pastures, to hauling cattle from pasture to packaging, and all of the manufactured consumables along the way. They take up a massive amount of resources that could be used elsewhere, but man are they tasty.
Yes a huge about of methane is produced by cattle as others have mentioned. [There is also an additional impact of deforestation as rain-forest is cut down to make way for new grazing pastures](https://rainforests.mongabay.com/0812.htm
) and high water usage, as well as opportunity cost associated with land being used for pasture. Depending on how you allocate the numbers and weight different factors, dairy and beef farming is one of the major contributors to agricultural global warming, which is similar in it's contribution to ALL transport (~13%). Edit: For clarification I do mean all agriculture makes roughly the same annual contribution as transportation.
There's an interesting documentary called Cowspiracy which addresses this.
The guy's numbers put methane at way more responsible for climate change than anything else, if he's right about the numbers, and also for how much water it costs and space is needed to raise livestock for food.
I don't know enough to challenge what he says, but the whole thing is an eye-opener.