There are many meanings of acceptance but in terms of grief, these are the meanings that are tied with the term "acceptance" in the 5 stages of grief/loss (this applies no matter what the loss is, whether a person, or a state of being we find ourselves in that wasn't where we wanted to be (loss of career, divorce, anything we have lost & have to deal with something else being the reality of our life):

1) Acceptance is often confused with the notion of being all right or okay with what has happened. This is not the case. Most people don't ever feel okay or all right about the loss of a loved one. This stage is about accepting the reality that our loved one is physically gone and recognizing that this new reality is the permanent reality. We will never like this reality or make it okay, but eventually we accept it. We learn to live with it. It is the new norm with which we must learn to live. This is where our final healing and adjustment can take a firm hold, despite the fact that healing often looks and feels like an unattainable state. (enotalone.com)

2) This is when the anger, sadness and mourning have tapered off. The person simply accepts the reality of the loss. (memorialhospital.org)

3) Accepting the loss does not mean forgetting or never feeling sad again, but it is a turning point that signals the final phase of grief has begun.

Acceptance is about understanding what has happened and that it cannot be changed. (gettingpastyourpast.wordpress.com - more about grief from the the loss of a relationship)

4) "It's going to be okay."; "I can't fight it, I may as well prepare for it."
In this last stage, the individual begins to come to terms with their mortality or that of their loved one.
Kübler-Ross originally applied these stages to people suffering from terminal illness, later to any form of catastrophic personal loss (job, income, freedom). This may also include significant life events such as the death of a loved one, divorce, drug addiction, the onset of a disease or chronic illness, an infertility diagnosis, as well many tragedies and disasters. (en.wikipedia.org)

5) Finally finding the way forward. (changingminds.org)

6) The bereaved person comes to terms with the loss, and is able to move on to re-invest in the new life that lies ahead.

Accepting the reality of the loss is the difficult work here. Initially the loss may be denied or minimized. Then it may be intellectually processed. The emotional recognition and acceptance of the loss is the most difficult to achieve, and involves a full recognition that the lost person will not return.

Talking about "recovering" from grief is almost disrespectful, as life is never restored to the way it was before the loss of someone close. When people talk of recovery, they really refer to overcoming grief and adapting to life after the death. This is an important distinction to draw, because the purpose of working through the grief stages is not to "get over" loss, but to adjust to its consequences, and restore balance.
(selfhelpmagazine.com)