Bonds are less risky, so having them in your portfolio is a "hedge" against market downturns. However, that's largely psychological; if you really want to lower your risk, you should just keep some of your portfolio as cash.
Another justification for them is that they are considered a separate "asset class", which means, among other things, that the correlation between stocks and bonds is significantly lower than within stocks, or within bonds. This increases diversification. It's not quite clear what you mean by "Or do bonds exist to maintain a portion of your portfolio during a market downturn?", but this might be what you mean: if there is a downturn in the stock market, then having bonds may reduce the impact somewhat. Of course, you'll be maintaining a portion of your portfolio during a market downturn no matter what anyway, unless you're heavily leveraged: the market has never lost all of its value.
Are bonds part of an investment portfolio so that you can invest during a dip in the market?
Again, it's not quite clear what you're saying here. You seem to be saying that if the stock market dips, then you can sell bonds and use the money to buy stocks. However, the Efficient Market Hypothesis says that the expected returns from the stock market after a dip are no larger than those without a dip.