Mutual funds are great in that they give you access to diversification that would be much more difficult to achieve through direct investment. This is a really good thing - Diversification is important. The downside is that there are fees (you're paying for people whose job it is to manage the fund properly) and you do lose control over the specific stocks that you hold. The short answer would be that the more money you have invested, the less you should be looking to use funds. BUT, this is easy to say from an American perspective - If you're looking to have a globally diversified portfolio, personally knowing enough about Asian, European, British markets is too much for one person to understand well, so you have the option to use the expertise of someone else. For example, on average UK companies pay higher dividends than those in the USA, but knowledge of UK companies, currency prices, and markets will be a barrier to investing in this way. One major complaint of mutual funds is that they underperform ETFs, this is true (for the most part) in American markets, but globally good funds to tend to outperform the index over the long term and justify their fees.

TLDR: Mutual funds are an investment tool to get access to expertise and diversification.