check the connection to the pipes under the sink. If your sink drains slowly also, then you have a clogged pipe that both drain from. Check you P trap.
Check your rubber hose from the washer to the sink pipes, is it crimped, bent, or clogged?
Check your strainer inside the washer for food buildup or an object that is restricting water empting.
My first thought was that you added a garbage disposal recently and did not knock out the knock out, but you said it did drain, but slowly.
Then, you might just have a bad water pump in the washer.
I am not a professional or a person of wisdom in this area, but common sense tells one to check the fittings, hoses, connections, and filter.
Hope some of this helps.
© 2016 Renovate Your World LLC