A Muslim woman must not be excessive in going out from home unless it is a valid necessity that cannot be fulfilled unless she goes out. So, if she has a need to go out, she must observe proper hijab. However, if a woman is able to stay at home, that is better and protective for her. Allah addressed His Prophet's wives-who are our role models -
"And remain in your homes." [Al-Azhaab:33]"

This is also reiterated when we read that Allah loves it when a woman prays at home and doesn't go to masjid though masjid is the pure place for prayer.

The Prophet (salallahu alayhi wassalam) said: Do not prevent the servant woman of Allah from going out to the masjid of Allah. But their homes are better for them." [Muslim no.442]

However, Scholars of Islam don’t restrict a woman from working outside of her home. In fact, there are jobs where women are required. For example, teaching women or female gynecologists, nurses etc.
 There is nothing wrong in that as long as she abides by the following guidelines:

She must have a need for doing this work or the community she lives in requires her to do this job, such that there cannot be found any man that can do the job.
She should do this after fulfilling the job she has at home, which is her primary job.
This job must be in an environment of women only, such as her teaching women (only) or doctoring and nursing female patients. And her work must be separate from men.

Likewise, there is nothing that restricts her from learning the affairs of her Religion – in fact, she is obligated to do this. And there is nothing preventing her from teaching about the aspects of her Religion, so long as there is a need for that and her teaching is held in an environment of (only) women. And there is no harm in her attending classes in a masjid and so on while being consistent in that and segregated from men.

 This can be seen from the women in the beginning of Islaam (i.e. the Sahaabiyaat), in that they would work and study and attend the masjid.
Also, since nowadays there are opportunities to work for a concern from home, this is good. It is also allowed by Islam provided she fulfills the job at home.