When you are hacking into a site, some actions you take can get you noticed, and eventually the automatic response kicks you out. This is represented by an "alert" value, which is listed on the left side pane.
The alert starts at zero, and slowly increases. For most sites, once it reaches 20-25, you get kicked off. Additionally, site defense Routines can activate, typically one at 6-8 alert and another 12-15 alert. Only one routine can activate each round; if you jump past multiple routine triggers in one round only the highest level routine within that range will activate.
Actions you do can be "unsubtle". See below for the math on how unsubtlety relates to alert increases.
Sources of Unsubtlety
Unsubtle functions
Functions are the only thing that explicitly state their unsubtlety values. For example, Brute Strike is 1 Unsubtle, so whenever you use Brute Strike in a batch, it adds one to the total unsubtlety that round.
Unsubtle Routine Response
When you target Routines, they can also increase the unsubtlety. These vary a lot of depending on the Routine and the functions used against it - see individual Routine pages for details. For example, if you use Offence against a Password Lock, it adds 2 more unsubtle, in addition to whatever unsubtle gained from the functions used to attack it.
Watcher Routine Responses
There are also some Routines which can actively observe your actions. For example, the Watching Eyes can "hone in on your disturbance", which gives one extra unsubtlety. This also depends on the functions used.
Reconnecting
You can choose spend a round reconnecting instead of targeting a Routine. This normally causes 1 unsubtlety, though Watcher Routines (see above) can increase that.
Converting Unsubtlety to Alert
At this point, you can add up all your sources of unsubtlety (Function Unsubtlety, Routine Unsubtlety and Watcher Unsubtlety) to get the Total Unsubtlety (TU). Then amount the Alert increases this round is then picked as a random number chosen between TU and 2xTU.
Incognito can modify this by a small amount. Positive Incognito can decrease the amount of Alert generated, while Negative Incognito can increases. More spading is needed here.
Example
You target a Password Lock with a Brute Strike. You gain 1 unsubtlety from using Brute Strike, and 2 unsubtlety from taking down a Password Lock. No watchers take notice so your Total Unsubtlety is 3. This means that the Alert will be raised by a random amount between 3 and 6.
With a high incognito, the resulting Alert is closer to 3 a lot more often than 6. With negative incognito, the Alert is 6 a lot more often than 3.