All of the e-mini index futures contracts trade on the quarterly expiration cycle. Contract Rollover occurs on the Thursday a week before the expiration Friday for the e-minis, this is the second Thursday of March, June, September and December. Each month is represented by a single letter:
H = March
M = June
U = September
Z = December
Since futures contracts expire, a position in an expiring contract, if it is to be continued, must be rolled to the next nearby futures contract. For an initial long (short) position, this means selling (buying) the expiring contract and buying (selling) the next contract.
There is usually a difference in price between the two contracts of a roll, referred to as the forward premium or discount (or spread) and this difference needs to be taken into account when calculating the unrealized profit or loss on a position or the setting of a protective stop order after the roll.
Both sides of the contract roll-over should be executed at the same time, otherwise it is referred to as "legging" into a position, and a spread order is typically used for this. In most cases, a spread order is entered as a market order but it can be specified as a limit order if the trader wants to have greater control over the spread price.
For deliverable futures contracts, which are most of them, a position should be rolled prior to the first notice day. The first notice day begins the delivery period and it is generally harder to roll a position once it is in the delivery period.
All positions, whether the contract is deliverable or cash settled, must be rolled prior to the last trading day. You should contact your broker to obtain a current schedule of these dates, referred to as an expiration calendar.
All open orders that are based on the expiring contract, for example, a protective stop order on the expiring contract, need to be canceled and replaced with new orders corresponding to the new contract after the roll. Keeping accurate records is a good way to not forget any such outstanding orders.
If you trade price and structure only, you can trade the continuous contract but if you trade price with order flow, you have to trade where the volume it's much easier to read. If you're not sure, simply don't trade rollover days until the volume of the new contract is much higher than the expiring contract.