Without knowing the details in the aforementioned example the number 1 reason for small trades is rebalancing.
Imagine a portfolio where 50% of the capital is in tech stocks and the other half in retail stocks. Now go one step into the future (a day, a week, a year, whatever): Your tech stocks might have advanced, say, 60% whereas your retailers, say, lost 20%. The capital is now distributed 2/3 in tech stocks and 1/3 in retailers.
If however you want to maintain the original 50/50 mix, for example because you're an ETF and promised your clients to do so, then now you'd have to sell some of your tech stocks and buy some retailers.
Of course there are various factors how you might end up with an imbalance (e.g. foreign currency exposure, dividends, shocks to volatility). When you're a fund or an ETF there's also the customer side of things: Imagine an additional investor that buys into your fund, say 0.1% of the fund's total volume. They want their cash performing like the rest of the fund so you'd have to buy 0.1% more of every stock you hold, and that might just amount to 15 shares.