I am not familiar with the term burn-beating, but from the description provided by Arvo M. Soininen, "Burn-beating as the technical basis of colonisation in Finland in the 16th and 17th centuries", Scandinavian Economic History Review, Vol. 7, No. 2, pp. 150-166 (scan online) the term appears to refer to slash-and-burn agriculture.
In slash-and-burn agriculture, (most of) the vegetation of an area is cut down and burned, with the resulting plant ash serving as fertilizer due to its mineral content, in particular potassium and phosphorus. Over the course of three to five years, the mineral content of the soil is depleted by successive crops, the field is abandoned, and cultivation moves to the next area. Fields created by slash-and-burn agriculture are therefore of a temporary nature. Soininen's paper describes multiple different methods of slash-and-burn agriculture practiced in Finland until quite recently.
In contrast, fields that, once created, are used for a long and indefinite period of time are permanent fields. Historically, such fields have been used continuously over time spans ranging from several decades to thousands of years. The abandonment of fields does occasionally occur due to any number of factors that make continued farming difficult, such as marginal soil or climate conditions or lack of manpower. Permanent fields require careful management of the soil to maintain its fertility. Historically this has involved crop rotation and fallowing (in which fields are allowed to "rest" for one or several years), irrigation, and fertilization by animal dung and / or vegetation matter taken from other areas (e.g. plaggen soil in parts of Northern Germany, or the use of seaweed in parts of Ireland).
The primary cereals for making bread are wheat and rye, while barley and oats may be mixed in. Historically significant portions of the rural population of Europe were sustained by cereal-based food in the form of gruel and porridge rather than by bread, especially prior to the introduction of the potato. Barley can be consumed in the form of pearl barley and groats and oats in the form of oatmeal. Especially in cool and humid climates not very suitable for cultivating wheat and rye, oats were once commonly cultivated and consumed. When Samuel Johnson wrote his dictionary, he famously defined oats as: "A grain which in England is generally given to horses, but in Scotland supports the people." A major historical and modern use of barley has been as malted barley, the main ingredient in beer brewing.
In the case of Finland it is interesting to note how late the transition from slash-and-burn agriculture to the use of permanent fields occurred. According to Teija Alenius, Environmental change and anthropogenic impact on lake sediments during the Holocene in the Finnish − Karelian inland area, Ph.D. thesis, University of Helsinki, 2007 (online)
Another study question concerns the relationship between slash-and-burn cultivation and permanent field cultivation. According to historical records, slash-and-burn cultivation remained the major method of cereal-crop cultivation in eastern Finland until the late 19th century (Soininen 1974). Permanent Iron Age fields, found at the city of Mikkeli, suggest cultivation on permanent fields from the 7th century (Mikkola 2004). This finding is significant, because it is the easternmost permanent prehistoric field complex found in Finland and therefore has a great socio-economic value (Mikkola 2004; Mikkola and Talvio 2000).