plumbing horror!

so, basically, i put the washing machine on, then half an hour later, i heard this loud dripping noise, and i ran to the kitchen to see what was going on.
somehow both the sinks(we have 2 sinks connected to each other in the kitchen) had been completely filled with water, soapy water, and were overflowing.
i was like ahhhhh did i leave the tap running?!!!!, but no, i hadnt.
there was a huge river on the kitchen floor, and it was increasing in speed towards the kitchen door, which leads to the living room, and i was freaking the hell out.
i thought oh no, itsd the washing machine leaking onto the floor, so i turned it off.
i then took the plugs out of the sinks, yet they wouldnt drain, so i got the plunger, but still, to no avail.
i then managed to figure out, although im not quite sure how, that i neede to drain the washing machine filter.
and somehow, me draining this, then caused the water in the sinks to slowly disperse.
it took 4 bucket fulls and over an hour, of me on my hands and knees, draining the filter to get the water to go down.
can anyone explain what the hell happened?how can the water somehow fill up the sinks?it doesnt make sense.im completely confused.
and i had sore and wet knees, and a lot of panic.
about 10 dishcloths and 2 mops later, the floor was still wet.
hence the flipflops.
but seriously...how did it happen?!