A nest egg is an amount of money or assets that you accumulate over time for a specific purpose. If you want in the future to buy a house or to retire early or with more money, then you can build your nest egg for that particular objective.
Nest Egg Explained
You can start by just saving some money out of your monthly paycheck and putting that money to work in low-risk investments like index funds, bonds, real estate and so on. The goal is to grow your saved money steadily over time.
For example, a classic investment is in an index fund tracking the S&P500 that historically returned 10% on average per year and with dividend reinvestments it’s even a little bit more.
Since you want to take advantage of the compounding effect, you should put aside only the money that you will not need and will not touch for a long time. This way when you decide after years to open your nest egg, you will enjoy the fruits of your investments.