In answer to your question, NO -- you do not get taxed on the funds remaining in the LLC. That's not how it works.
Recall that LLCs have what's called "pass-through" taxation unless you've elected to be taxed as a corporation. So, think of it like you would if you were a sole-proprietor: You put, say $50,000 into the company, it spends $20,000 in expenses and makes $120,000 in revenue. At the end of the day, the company has $50k - $20k + $120k = $150,000. The increase of $100,000 is taxable to you.
Now, let's say you owned the same company equally with somebody else, a 50/50 split, where you each originally put in $25,000. Under the most common setup for LLCs, half of the increase is allocated to you, and half is allocated to him. You each owe tax on $50,000.
Now, let's say that you're really the only person working the company. So, you need to be paid something--say $40k--for the services you provide to the company. You set this up as a "guaranteed payment", which is taxable to you, but gets deducted from what the company has. So, instead of having $150k, it only has $110k. Now, the $60k increase ($110k - $50k = $60k) is taxable to the two of you equally. So, you're taxed on $70k (the $40k + 1/2 the $60k), and your partner is only taxed on the other $30k.
Change it again -- say that both of you are working the business, but that you need more cash than your partner does. (Maybe you have a family and he's single). So, at the end of the year, you take out $40k. You can do that because you originally put in $25k and half the profit ($50k) is allocated to you. for a total of $75k. So you take a distribution from the company. As a result, the Company now has $110k. However, that money is not equally allocated between you and your partner -- $75k of that is considered to be his; the remaining $35k is considered to be yours.
[Note, however, that I said "under the most common setup" -- it's possible to set up the LLC with other schemes. But, to understand all the variations, you literally need a graduate course in partnership taxation, which is a complicated area of tax law.]